Higher power moments of exponential sum with twisted divisor function
Abstract
Suppose that χ \chi be a non-principal even primitive character modulo q 1 q_1 and d χ ( n ) = ∑ l | n χ ( l ) d_{\chi }(n) = \sum _{l|n} \chi (l) . In this paper, we evaluate ∫ 0 1 | M χ ( α ) | s d α \int _0^1 |M_\chi (\alpha )|^s d\alpha for any real number s > 2 s> 2 , where M χ ( α ) = ∑ n ≤ X q 1 d χ ( n ) e ( n α ) M_\chi (\alpha ) = \sum _{n \leq Xq_1} d_{\chi }(n)e(n\alpha ) , and e (
Fields of Study & Subjects
Analytic Number Theory Research
Advanced Mathematical Identities
Mathematical Approximation and Integration
Publication details
- Journal / source
- Proceedings of the American Mathematical Society
- Publication date
- 5 March 2026
- Language
- EN